Details

analyze459.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
25%	74.9%	0.1%	6
25%	68.6%	6.4%	7
31.2%	62.4%	6.4%	8
36.7%	54.6%	8.7%	9
38.2%	48.4%	13.4%	10
42.7%	42.3%	15%	11
47.8%	34.1%	18.1%	12
49.1%	30.3%	20.5%	13
51.9%	25.8%	22.3%	14

sample39.0ms

Algorithm

intervals

Results

9.0ms	167×	body	80	valid
8.0ms	28×	body	2560	valid
7.0ms	28×	body	1280	valid
3.0ms	15×	body	640	valid
1.0ms	9×	body	320	valid
1.0ms	3×	body	5120	valid
1.0ms	13×	body	80	nan
1.0ms	6×	body	160	valid
1.0ms	10×	body	80	invalid

simplify312.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1803	24
1	1803	24

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.7b

Counts

2 → 1

localize9.0ms

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series271.0ms

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) b) (.f64 3 a))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
68.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))) b)
65.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify85.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4899	1967
1	4899	1967

prune103.0ms

Filtered

62 candidates to 82 candidates (-32.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	73	9	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	9	83

Merged error: 6.7b

Counts

83 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
2.2b	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
12.6b	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
17.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
11.0ms	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series484.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
155.0ms	(/.f64 (/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
210.0ms	(/.f64 (.f64 (.f64 a c) -3) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify90.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5006	3204

prune108.0ms

Filtered

78 candidates to 114 candidates (-46.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	3	5	8
Picked	1	0	1
Done	0	0	0
Total	115	8	123

Merged error: 6.6b

Counts

123 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (neg.f64 (/.f64 1 c))))
1.0b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-exp-log_binary64`
9×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `pow1_binary64` `add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r/_binary64`
4×	`div-exp_binary64`
3×	`flip3-+_binary64` `distribute-neg-frac_binary64` `prod-exp_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `rec-exp_binary64` `flip--_binary64` `pow-flip_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-/r_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

12.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (neg.f64 (/.f64 1 c))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series300.0ms

Counts

4 → 12

Calls

4 calls:

139.0ms	(/.f64 1 (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (neg.f64 (/.f64 1 c))))
35.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
62.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
64.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify71.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4941	1753
1	4941	1753

prune77.0ms

Filtered

59 candidates to 83 candidates (-40.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	82	9	91

Merged error: 6.6b

Counts

91 → 9

localize12.0ms

Local error

Found 4 expressions with local error:

1.4b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
2.2b	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
12.7b	(/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
23.7b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`times-frac_binary64`
21×	`*-un-lft-identity_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64` `associate-/l*_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64` `pow1_binary64` `distribute-lft-out_binary64`
4×	`flip3-+_binary64` `div-inv_binary64` `flip-+_binary64`
3×	`sqrt-prod_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 102

Calls

4 calls:

8.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
14.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
12.0ms	(/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

series479.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
149.0ms	(/.f64 (/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 a -3))
201.0ms	(/.f64 (.f64 (.f64 3 a) c) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4898	3185
1	4898	3185

prune97.0ms

Filtered

77 candidates to 114 candidates (-48.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	114	9	123

Merged error: 6.6b

Counts

123 → 9

regimes147.0ms

Accuracy

95.2% (1.2b remaining)

Error of 6.5b against oracle of 5.3b and baseline of 29.9b

bsearch106.0ms

Steps

Iters	Range	Point
9	1.1344390662495468e+105	7.881912223752934e+111	2.217223282760919e+108
9	-2.1302178015190597e-218	-9.26767730910889e-224	-4.704826106702257e-221
8	-4.073691251659333e+151	-3.8070823667357286e+148	-2.097183452461109e+149

Iters

Range

Point

1.1344390662495468e+105

7.881912223752934e+111

2.217223282760919e+108

-2.1302178015190597e-218

-9.26767730910889e-224

-4.704826106702257e-221

-4.073691251659333e+151

-3.8070823667357286e+148

-2.097183452461109e+149

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	207	92
1	207	92

end0.0ms

sample1.2s

Algorithm

intervals

Results

317.0ms	1077×	body	2560	valid
273.0ms	5119×	body	80	valid
219.0ms	910×	body	1280	valid
82.0ms	424×	body	640	valid
41.0ms	111×	body	5120	valid
37.0ms	245×	body	320	valid
37.0ms	615×	body	80	nan
18.0ms	338×	body	80	invalid
11.0ms	114×	body	160	valid

Details

analyze459.0ms

sample39.0ms

simplify312.0ms

prune4.0ms

localize9.0ms

rewrite30.0ms

series271.0ms

simplify85.0ms

prune103.0ms

localize13.0ms

rewrite42.0ms

series484.0ms

simplify90.0ms

prune108.0ms

localize13.0ms

rewrite29.0ms

series300.0ms

simplify71.0ms

prune77.0ms

localize12.0ms

rewrite43.0ms

series479.0ms

simplify92.0ms

prune97.0ms

regimes147.0ms

bsearch106.0ms

simplify6.0ms

end0.0ms

sample1.2s

Profiling